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If so, where a violation of this relationship is observed on market smiles, can it be arbitraged? These are the issues we address in this chapter, for general stochastic volatility models based on diffusion processes. indd 3 11/03/2013 10:09 post-crisis quant finance which will prompt us to introduce a new quantity: the skew stickiness ratio (SSR). In the second section, we address the issue of practically materialising the profit and loss (P&L) resulting from a difference between implied and realised SSR, focusing on short maturities.
9) f is a linear combination of exponentials: as T → ∞, f(u) ∝ e−min (k )u. Thus, when T → ∞, ST ∝ 1/T and RT → 1, the model eventually i i behaves like type I. 2 ln(ST . 0 0 2 4 6 8 10 possible to generate a power law-like behaviour for f over a sufficiently wide range of maturities. 36, which are typical of equity index skews and volatilities of volatilities. 9. 2 shows the 95/105 skew defined as ST . ln(95/105) as a function of T in log/log plot, for maturities from three months to five years.
Multi-curve environments, collateralisation of trades, the effects of new regulation and the uncertainty associated with it, and the awareness of the flaws in risk measurement, are all components of a new reality whose foundations have been laid in the past four years. I trust the reader with find the ideas in this book both inspiring and constructive. Mauro Cesa REFERENCES Andreasen, J. and B. Huge, 2013, “Expanded Local Volatility,” Risk, January. Basel Committee on Banking Supervision (BCBS), 2010, "Basel III: A Global Regulatory Framework for more Resilient Banks and Banking Systems," December.